I put this here partially so people might see it but also just to remind myself
that it's something I want to ask myself.

The "FI" in "FIP" stands for "fielding independent" (hyphen?) because it uses
only walks, strikeouts, and homers as inputs, none of which actions involve any
fielder not wearing a mask.1 Fielders, however, have significant input
on the question of whether balls put in play result in men running the bases.
So: do pitchers rack up walks, strikeouts, and homers differently with men on
base?

Note, of course, that we had better not simply answer this question by looking
at league splits -- the pitchers who pitch with men on base most often are sure
to be worse than the pitchers who don't.

If there is a difference, is it a difference that's big enough that that we
should be calling it Q(uasi)FIP?

Is the Q/FIP question, assuming one exists, just a linguistic one? Could we gain
more accuracy by attempting to strip out these effects? Enough accuracy to make
it worth the additional complexity?

One obvious exception is dropped foul pops that extend at-bats, creating
walks and strikeouts and homers that should have been flyouts. Another
less obvious one is very short homers that are narrowly brought back (or
not) by a leaping outfielder. These are such aberrant situations,
though, that they presumably only affect the "FI"-ness of FIP at the
type of minute level that it's foolish to measure baseball at anyway. ↩